When I say "God is good", I mean it in both senses the English sentence indicates:
- God is morally upright, or blameless. God doesn't ever do anything wrong, He is completely right. You and I have certainly done things we knew were wrong. Everyone has. God hasn't. Ever. Not once. The Biblical term for this is sense of good is "righteous".
- God is kind. God does kind things for us, at great personal cost.
The history of the Gospel is something like this: Jesus Christ, the Son of God, came down here to earth, walked around for 30-something years; and then was beaten and crucified by the people of His time. He was buried, and on the third day, He was raised from the dead. He spoke to several hundred people over some 40 days, then was taken up into Heaven in the sight of several people.
How does this infer God's goodness?
First, it demonstrates our own badness. Jesus Christ did nothing that wasn't good. He healed people, provided food for them, and taught them. He never did anything that was less than perfect. And what did we do? We (I use the term to mean people in general) beat Him, hung Him on a cross, and left Him to die. Consider that for a moment: we abused and crucified the Son of God. When we consider just how bad we are, we are shocked to see that God cares about us. This is the goodness of God: He, knowing how bad we are, wants us to be with Him.
Second, it demonstrates the price He was willing to pay for us. While we frequently say "Salvation is free"; the fact of the matter is, it wasn't free for Him. Our right to come into God's presence was very, very costly. It was unimaginably costly. None of us would honestly say it was a good idea, if the truth were known. But the goodness of God is this: God thought it was worthwhile to give the priceless to buy the worthless.
Third, it demonstrates His refusal to compromise. God was unwilling to compromise His goodness in either direction: He didn't balk at saving sinners, but He also didn't take an easy way out. Anyone else would have either abandoned the whole idea and just let us burn in Hell; or would have come up with some sort of compromise "Don't worry about that whole sin thing...". The goodness of God is: God looked unflinchingly at the cost of bringing sinners to Heaven, and paid it.
God's goodness is demonstrated in that He saves sinners, but not by compromising His own righteousness.